few_shots: Example:
Problem/activity:
For each pair of numbers, determine if the values are equivalent. Explain your reasoning for each one.
a.
$$-0.25$$
and
$$\frac{1}{-4}$$
b.
$$-\left ( \frac{1}{4} \right )$$
and
$$\frac{-1}{-4}$$
c.
$$\frac{-1}{4}$$
and
$$-\frac{1}{4}$$


Mathematical concept/skill options: 
A. Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
B. Reason quantitatively and use units to solve problems.
C. Apply and extend previous understandings of numbers to the system of rational numbers.
D. Represent complex numbers and their operations on the complex plane.
E. Perform arithmetic operations with complex numbers.
F. Compute fluently with multi-digit numbers and find common factors and multiples.
G. Represent and model with vector quantities.
H. Perform operations on vectors.
I. Use properties of rational and irrational numbers.
J. Use complex numbers in polynomial identities and equations.
K. Extend the properties of exponents to rational exponents.
L. Know that there are numbers that are not rational, and approximate them by rational numbers.
M. Perform operations on matrices and use matrices in applications.
N. Apply and extend previous understandings of multiplication and division to divide fractions by fractions.


Thought: This problem involves understanding fractions, multiplication, and division.
Answer: A

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: fl_problem_001097

7
options: Understand the place value system.

Use place value understanding and properties of operations to add and subtract.

Generalize place value understanding for multi-digit whole numbers.
Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.

Work with numbers 11–19 to gain foundations for place value.

Use place value understanding and properties of operations to perform multi-digit arithmetic.
Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.

Extend the counting sequence.

Use place value understanding and properties of operations to perform multi-digit arithmetic. (A range of algorithms may be used.)

Understand place value.

Perform operations with multi-digit whole numbers and with decimals to hundredths.
problem_activity: Problem 1
a.   How many do you see? How do you see them?
[IMG]
b.   Instead of writing
$$10 \times 10$$
, we can write
$$10^2$$
, which we read “ten to the
power
of two.” The two is the
exponent
and tells us how many times we multiply 10 by itself. How would you represent the number of the smallest spokes in the image above as a power of 10?
Problem 2
a.   Write each of the following as a product of tens and in standard form.
$$10^4$$
$$10^6$$
b.   Write each of the following as a power of 10.
10 × 10 × 10 × 10 × 10
1,000,000,000
Problem 3
a.   Solve.
10 × 10,000 = ______
1,000 × 1,000 = ______
1,000,000 × 100 = ______
b.   How were powers of 10 useful in solving Part (a)?


correct_option_index: 0